Before proceeding, we pause to make two comments of a technical nature. In what follows, we
express the masses
and decay constants of composite states in units of the lattice spacing \(a\) .
The reader might, with some reason, think that it
would be best practice to introduce a non-perturbative scale-setting procedure that
allows to take the continuum \(a\rightarrow 0\)  limit without ambiguities. And indeed,
in previous publications
our collaboration elected to
adopt to this purpose the Wilson flow [1]}, [2]}.
Yet, as in this work we do not attempt the continuum limit extrapolation, but rather only extract
lattice measurements in a small number of ensembles, this is not necessary.
Furthermore, in this theory the fermions have
non negligible dynamical effects—see for example Fig. REF —and hence the Wilson flow observables
are expected to be quite sensitive to the choice of fermion mass, making a future, dedicated study necessary.
We plan to do so when we will have enough numerical ensembles to perform
the continuum and chiral limit extrapolations.
